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<p>We develop a score-driven time-varying parameter model where no particular parametric error distribution needs to be specified. The proposed method relies on a versatile spline-based density, that produces a score function in the form of a natural cubic spline. This flexible approach nests the Gaussian density as a special case. It can also represent asymmetric and leptokurtic densities that produce outlier-robust updating functions for the time-varying parameter and that are often used in empirical applications. As leading examples, we consider models where the time-varying parameters appear in the location or in the log-scale of the observations. The static parameter vector of the model can be estimated by the maximum likelihood method and we formally establish some of the asymptotic properties of such estimators. We illustrate the practical relevance of the proposed method in two empirical studies. We employ the location model to filter the mean of the U.S.&#xa0;monthly CPI inflation series and the scale model for volatility filtering of the full panel of daily stock returns from the S&amp;P 500 index. The results show a competitive performance of the method compared to a set of competing models that are available in the existing literature.</p>

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Score-driven time-varying parameter models with spline-based densities

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  • 出版模式：

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  • 发表日期：

    2026年2月24日

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  • Janneke van Brummelen,
  • Paolo Gorgi,
  • Siem Jan Koopman

摘要

We develop a score-driven time-varying parameter model where no particular parametric error distribution needs to be specified. The proposed method relies on a versatile spline-based density, that produces a score function in the form of a natural cubic spline. This flexible approach nests the Gaussian density as a special case. It can also represent asymmetric and leptokurtic densities that produce outlier-robust updating functions for the time-varying parameter and that are often used in empirical applications. As leading examples, we consider models where the time-varying parameters appear in the location or in the log-scale of the observations. The static parameter vector of the model can be estimated by the maximum likelihood method and we formally establish some of the asymptotic properties of such estimators. We illustrate the practical relevance of the proposed method in two empirical studies. We employ the location model to filter the mean of the U.S. monthly CPI inflation series and the scale model for volatility filtering of the full panel of daily stock returns from the S&P 500 index. The results show a competitive performance of the method compared to a set of competing models that are available in the existing literature.